Thank you, guys.
Indeed, it seems R-N803 best for the money in that case.
My further research found this thread very interesting as well.
www.avsforum.com
The two share the most critical part that determines the final audio spec, that is the volume control IC. Besides that, the A-S801 has a marginally better DAC, the ES9010KS2 vs the ES9006 in the R-N803 and it can be used as an USB DAC.
That's why I rarely suggest the A-S801 to those asking about integrated amps, because the 801 is more like an AVR, or the R-N803 without the tuner and the video stuff, with virtually nothing value added to the audio side.
It does seem to have implemented the DAC better (balanced mode) so my educated guess is that its THD+N may measure a few dB better (just may be). That's assuming the R-N803 does not use the balanced mode, that the older generation R-S700 did, according to hometheaterhifi.com.
Regardless, those who claimed the A-S801 "sounds better", I would bet 2:1 in a blind comparison, they would not be able to tell the two apart. Very few people could tell the difference between THD+N of say -95 dB vs -90 dB, even in anechoic chamber, that's just science. Golden ears can because they also use their eyes to enhance their hearing.
If the USB DAC, and the look matters, go for the 801, otherwise the R-N803 is clearly a better value. For those who wants a real integrated amp, the A-S700 or R-S700 would be the better choices, if you can find one.